On a windy autumn day, an acorn falls from a branch of a giant oak tree. The acorn's height above the ground in feet can be modeled by the expression 80 - 16t^2, where t is the time in seconds after the acorn begins to fall. What does the quantity 16t^2 represent in the expression? Choices: (A)the height in feet of the acorn after t seconds (B)the distance in feet the acorn has fallen after t seconds (C)the time in seconds it takes for the acorn to fall t feet (D)the time in seconds it takes for the acorn to reach a height of t feet

Question

On a windy autumn day, an acorn falls from a branch of a giant oak tree. The acorn's height above the ground in feet can be modeled by the expression 80 - 16t^2, where t is the time in seconds after the acorn begins to fall. What does the quantity 16t^2 represent in the expression?   Choices: (A)the height in feet of the acorn after t seconds (B)the distance in feet the acorn has fallen after t seconds (C)the time in seconds it takes for the acorn to fall t feet (D)the time in seconds it takes for the acorn to reach a height of t feet

Bytelearn · Accepted Answer

Expression for Acorn's Height: The expression for the acorn's height is 80 - 16t^2. Since the acorn is falling, the height decreases over time.Interpretation of 16t^2: The term 16t^2 must represent the distance the acorn has fallen after t seconds, because as time increases, this term increases, which would decrease the overall height from the starting point of 80 feet.Initial Height of Acorn: The initial height of the acorn is 80 feet, so 16t^2 cannot represent the height of the acorn after t seconds, because it doesn't include the initial height.Limitations of 16t^2 Term: The term 16t^2 also cannot represent the time it takes for the acorn to fall t feet or to reach a height of t feet, because it's a quadratic term and time is linear in this context.

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